Simply put, the feature that allows the Project/Properties windows on the sides of Construct to auto hide/show stops showing the windows after you have previewed your game. After a preview, hover or even clicking won't show the window until I have switched to another event sheet or layout editor first.
Are you previewing fullscreen or windowed? I can't imagine how a windowed preview would do this.
I was previewing windowed, but if you've been keeping tabs on the bugs that happen to me they're usually wildly random, and as such the bug isn't happening to me right now...
I've created a circumstance where the bug always happens. If I rename an animation having both Properties and Animator to hide automatically and when I finish the animation name by pressing Enter, it will make the auto-reappear stop working until I've switched to a different event sheet or layout editor.
It happens with all input fields in the Properties window and pressing Enter.